Question

eyeglassomatic manufactures eyeglasses for different retailers. they test lenses in a given time period to check for defects. of the 20 they found with defects, they classified each of them by the type of defect (scratched, wrong shape or size, spots or bubbles, other). the results are in the table below.
scratched
scratched
scratched
wrongshapesize
wrongshapesize
wrongshapesize
other
wrongshapesize
scratched
wrongshapesize
wrongshapesize
other
wrongshapesize
spotsbubbles
spotsbubbles
wrongshapesize
spotsbubbles
wrongshapesize
spotsbubbles
other
a) since data were collected for? select an answer variable(s), the correct graph to make is a select an answer.
b) complete the frequency/relative frequency table.
defect type frequency relative frequency
scratched
wrongshapesize
spotsbubbles
other

Explanation:

Step1: Identify number of variables

There is 1 categorical variable (defect type), so a bar - graph is appropriate.

Step2: Count frequencies

Count the number of times each defect type appears in the data. Scratched appears 4 times, WrongShapeSize appears 9 times, SpotsBubbles appears 4 times, and Other appears 3 times.

Step3: Calculate relative frequencies

The total number of defects is $n = 20$. The relative frequency of a category is calculated as $\text{Relative Frequency}=\frac{\text{Frequency}}{\text{Total Frequency}}$.
For Scratched: $\text{Relative Frequency}=\frac{4}{20}=0.2$
For WrongShapeSize: $\text{Relative Frequency}=\frac{9}{20}=0.45$
For SpotsBubbles: $\text{Relative Frequency}=\frac{4}{20}=0.2$
For Other: $\text{Relative Frequency}=\frac{3}{20}=0.15$

Answer:

a) 1; bar - graph
b)

Defect Type	Frequency	Relative Frequency
WrongShapeSize	9	0.45
SpotsBubbles	4	0.2
Other	3	0.15